A smooth, complex generalization of the Hobby-Rice theorem

The Hobby-Rice Theorem states that, given $n$ functions $f_j$ on ${\mathbb{R}}^N$, there exists a multiplier $h$ such that the integrals of $f_jh$ are all simultaneously zero. This multiplier takes values~$\pm1$ and is discontinuous. We show how to find a multiplier $h=e^{ig}$ that is infinitely differentiable, takes values on the unit circle, and is such that the integrals of $f_jh$ are all zero. We also show the existence of $n$ infinitely differentiable, real functions $g_j$ such that the $n$ functions $f_j e^{ig_j}$ are pairwise orthogonal.Comment: 8 pages, latex. Version V3 has an additional corollary 1.3 plus improved abstract, corrected typos and added reference

Cocommutative coalgebras: homotopy theory and Koszul duality

We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.Comment: 38 page

Justification for the decision on loading channels of the network of geoecological monitoring of resources of the agroindustrial complex

The article is devoted to solving an urgent scientific and technical problem. It consists of developing an algorithm .This is used for estimating the recommended buffer size of requests of transmitting data streams. So,this has been done in a flying self-organizing network .Therefore, it is used to ensure geoecological monitoring of the resources of the agro-industrial complex. However, Studies have shown that to ensure the required quality of data streams transmission. Thus, it is advisable to carry out preliminary reservation of channel performance. Hence, it is possible to increase the likelihood of servicing requests of the transmission of data streams, as well as to increase the load of network channels by buffering incoming requests of the transmission of data streams. So, the developed algorithm makes it possible to substantiate the decision-making to increase the channel load and ensure an acceptable delay in the start of data streams transmission .Therefore ,it has been done in a flying self-organizing network. Hence, the studies carried out the correctness of the algorithm and the expediency of its application. However, in practice the process of tuning the channels of a flying self-organizing network has been carried

Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory

The magic proton and neutron numbers are searched in the superheavy region with proton number $Z$=100 - 140 and neutron number $N$= ($Z$+30) - (2$Z$+32) by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies $S_{2p}$ and $S_{2n}$, the two-nucleon gaps $\delta_{2p}$ and $\delta_{2n}$, the shell correction energies $E_{shell}^{p}$ and $E_{shell}^{n}$, the pairing energies $E_{pair}^{p}$ and $E_{pair}^{n}$, and the pairing gaps $\Delta_{p}$ and $\Delta_{n}$, $Z$=120, 132, and 138 and $N$=172, 184, 198, 228, 238, and 258 are suggested to be the magic numbers within the present approach. The $\alpha$-decay half-lives are also discussed. In addition, the potential energy surfaces of possible doubly magic nuclei are obtained by the deformation-constrained relativistic mean field (RMF) theory, and the shell effects stabilizing the nuclei are investigated. Furthermore, the formation cross sections of $^{292}_{172}$120 and $^{304}_{184}$120 at the optimal excitation energy are estimated by a phenomenological cold fusion reactions model with the structure information extracted from the constrained RMF calculation.Comment: 37 pages, 14 figure

Colonic ulcerations may predict steroid-refractory course in patients with ipilimumab-mediated enterocolitis

To investigate management of patients who develop ipilimumab-mediated enterocolitis, including association of endoscopic findings with steroid-refractory symptoms and utility of infliximab as second-line therapy

Shell structure of superheavy nuclei in self-consistent mean-field models

We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic models show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%-80%. Spherical doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or (Z=126,N=184) depending on the parameterization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in Pb208. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for (Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.Comment: 22 pages REVTeX, 16 eps figures, accepted for publication in Phys. Rev.

Anisotropic Magnetoconductance in Quench-Condensed Ultrathin Beryllium Films

Near the superconductor-insulator (S-I) transition, quench-condensed ultrathin Be films show a large magnetoconductance which is highly anisotropic in the direction of the applied field. Film conductance can drop as much as seven orders of magnitude in a weak perpendicular field (< 1 T), but is insensitive to a parallel field in the same field range. We believe that this negative magnetoconductance is due to the field de-phasing of the superconducting pair wavefunction. This idea enables us to extract the finite superconducting phase coherence length in nearly superconducting films. Our data indicate that this local phase coherence persists even in highly insulating films in the vicinity of the S-I transition.Comment: 4 pages, 4 figure RevTex, Typos Correcte

A proposed reaction channel for the synthesis of the superheavy nucleus Z = 109

We apply a statistical-evaporation model (HIVAP) to calculate the cross sections of superheavy elements, mainly about actinide targets and compare with some available experimental data. A reaction channel $^{30}$Si + $^{243}$Am is proposed for the synthesis of the element Z = 109 and the cross section is estimated.Comment: 4 pages, 2 figures, 2 tables; two typos are corrected in Ref. [12] and [19